Question

Thermodynamics of a single molecule:

One end of a molecule is fixed to a surface. Another end is pressed down by the tip of an atomic force microscope, as shown below. Using the tip of an atomic force microscope as a probe, we measure the force of molecule retraction. The force depends on the temperature at which the experiment is performed: f= (aT+b) x where a and b are constants

(a) Using the thermodynamic identity for U (i.e. dU= T dS-p dV+μ dN+f dx) for the system, write the thermodynamic identity for G at constant N.

(b) Find a partial derivative equation from the equation you got in (a) at constant T and P and use it to find an expression for G (hint: integrate)

(c) Find a Maxwell relation to express ( ??/??) ?,? ; from the expression, find S(x) at constant T and P.

(d) Using the partial derivative expression you got in (b) and Maxwell relation from (c), find an expression for enthalpy H at fixed T and P.

Answer 1